Ancient-Red-Dragon: One could just as easily say that things like doing in-game sidequests, or getting a fast completion time (in speed-based games), or getting a high score (in score-based games), or fulfilling the requirements of in-game checklists, or even just completing a game's main story, is equally as pointless as is the act of earning Achievements.
If you truly believe as such, then there's really no point for you in playing video games.
Story-based sidequests - you're experiencing content that enhances the experience of the main storyline game. Maybe there's more character development/progression with one of your side characters, maybe it adds more storytelling to the subtext of the game's message, maybe it deepens the world's lore, maybe it adds a higher difficulty gameplay, or maybe there are hints from the devs that there'll be another sequel. This isn't equivalent to a small popup window saying you got an achievement.
Speedrunning - your name is on record and you're acknowledged by the speedrunning community. If you're really good, you might be showcased in a documentary by Youtubers like Summoning Salt or Abyssoft. You can cheat achievements with Cheat Engine or what-have-you, but you can't cheat a speedrun because others will check and do the math that your runs are legitimate. This isn't equivalent to a small popup window saying you got an achievement either.
But some people have fun earning Achievements, just like the fun that they & others have from other aspects of playing the games.
Who's to say that "non-Achievement fun" is 'right & good' and "Achievement fun" is 'wrong & bad'...?
Having said that, I do agree that some Achievements are needlessly repetitive & grindy, just for the sake of being repetitive & grindy, and those particular Achievements are indeed unhealthy. But that doesn't mean that the concept of Achievements itself is bad; it just means that some Achievements are poorly-designed & implemented.
Sure, some people can have their fun with achievements in a healthy manner. And some devpubs actually know how to make good achievements that can enhance the player experience. I don't have a problem with in-game achievements and those who enjoy achievements and can politely ask the devpubs for them.
However, it's in the way it's been implemented in modern times that is problematic. Instead of them being in-game, they are now tied to server-side clients as MysterD said. It encourages people susceptible to achievement obsession to use clients. I've discussed before how Steam has in its documentation how they urge devpubs to create achievements through Steamworks as a way to "enhance the value of legitimate copies" and have cited Heartbound by Pirate Software that tied their client achievements with their save system so that the game is effectively DRM'd. So ultimately, it is one of many vehicles that Steam and pro-DRM devpubs use to build user dependency on clients, and slowly enact their DRM creep.
As for GOG specifically, AB2012 has commented multiple times on why it's been a negative externality for offline installer users. Achievements being tied to clients means devpubs have to jump through more hoops to distribute here, Galaxy's Steam Wrapper Beta is in an abysmal state that slows game launch times by 3-6x because they're searching for Galaxy to be open. It's bad for prospective devpubs, it's bad for offline installer users - the implementation is just too much of a hassle for something that is entirely optional and is ephemeral. Because we all know that if/when any platform dies, their achievements will die with them even if you were to screenshot it beforehand. And that touches on why most of us are on GOG in the first place - the offline installers are what will last forever, not the client that achievements are tied to. We shouldn't be putting the cart before the horse.
And finally there are achievement extremists such as yourself, who demand achievements and slander legitimately good games simply because they lack them. It dissuades devpubs who do read the release threads from releasing more of their titles here and further sets the DRM-free movement further back into the stone ages. We've already seen this with Axiom Verge devs who felt pressured release achievements with their GOG port and ultimately decided not to. It worsens the store for the rest of us and that is something me and others here are not OK with.
If you can consider being less inflammatory with your demands and asking more nicely like most reasonable people, you'd have a lot more sympathy for your cause.